Back to Aristotle!

Hartley Slater

DOI: http://dx.doi.org/10.12775/LLP.2011.017

Abstract


There were already confusions in the Middle Ages with the reading of Aristotle on negative terms, and removing these confusions shows that the four traditional Syllogistic forms of statement can be readily generalised not only to handle polyadic relations (for long a source of difficulty), but even other, more measured quantifiers than just ‘all’, ‘some’, and ‘no’. But these historic confusions merely supplement the main confusions, which arose in more modern times, regarding the logic of singular statements. These main confusions originate in the inability of the mainline modern tradition to supply the ‘logically proper names’ which alone have the right to replace individual variables; an inability which has resulted in the widespread, but erroneous replacement of individual variables with ordinary proper names, i.e. names for contingent beings, in many if not most contemporary logic texts. The paper includes the exhibition and grammatical characterisation of the logically proper names that are required instead, specifying just how they differ syntactically from ordinary proper names. It also shows how ontologically significant is the distinction, since not only do logically proper names refer to necessarily existent objects (showing there are no ‘empty domains’ for Classical Logic to fail to apply to), but also thereby central features of Realism become considerably clarified.

Keywords


logically proper names; Aristotelian logic; classical logic; free logic

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References


Prior, A. N., 1962, Formal Logic, O.U.P., Oxford.

Slater, B.H., 2009, “Hilbert’s epsilon calculus and its successors”, pages 385–448 in: D. Gabbay and J. Woods (eds.) Handbook of the History of Logic, vol. 5, Elsevier Science, Burlington MA.

Thompson, M., 1953, “On Aristotle’s square of opposition”, Philosophical Review 62: 251–265.








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